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Intermediate Algebra
Tutorial 41: Rationalizing Denominators and Numerators

 Step 1: Multiply numerator and denominator by a radical that will get rid of the radical in the denominator.

 Since we have a square root in the denominator,  we need to multiply by the square root of an expression that will give us a perfect square under the square root in the denominator.  So in this case, we can accomplish this by multiplying top and bottom by the square root of 11:

 *Mult. num. and den. by sq. root of 11     *Den. now has a perfect square under sq. root

 AND Step 3: Simplify the fraction if needed.

 *Sq. root of 121 is 11

 Step 1: Multiply numerator and denominator by a radical that will get rid of the radical in the numerator.

 Since we have a cube root in the numerator,  we need to multiply by the cube root of an expression that will give us a perfect cube under the cube root in the numerator.  So in this case, we can accomplish this by multiplying top and bottom by the cube root of :

 *Mult. num. and den. by cube root of      *Num. now has a perfect cube under cube root

 AND Step 3: Simplify the fraction if needed.

 *Cube root of 125 y cubed is 5y

 Step 1: Find the conjugate of the denominator.

 In general the conjugate of a + b is a - b and vice versa. So what would the conjugate of our denominator be? It looks like the conjugate is .

 Step 2: Multiply the numerator and the denominator of the fraction by the conjugate found in Step 1 .

 *Mult. num. and den. by conjugate of den. *Product of the sum and diff. of two terms

 AND Step 4: Simplify the fraction if needed.

 No simplifying can be done on this problem so the final answer is:

Last revised on July 21, 2011 by Kim Seward.